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Yukawa shook his head—a barely perceptible movement—then came to sit down across from Kusanagi. “The last time I met Ishigami, he presented me with a mathematical conundrum,” he said. “It’s a famous one, the P = NP problem. Basically, it asks whether it’s more difficult to think of the solution to a problem yourself or to ascertain if someone else’s answer to the same problem is correct.”

Kusanagi frowned. “That’s mathematics? Sounds more like philosophy.”

“Bear with me. By turning himself in, and giving you his testimony, Ishigami’s presented you with an answer that, no matter how you look at it, has to be correct. If you just nod your heads and say, ‘Okay, sounds good to us,’ you’ve lost. Really, what you should be doing is putting all your efforts into determining whether his answer is correct or not. It’s a challenge. You’re being tested.”

“And like I said, we looked into it. Everything backs up his story.”

“All you’re doing is tracing the steps of his proof. What you should be doing is looking to see if there aren’t any other answers that might fit what you know about this case as well. Only if you can prove that there are no legitimate answers other than the one he’s offered can you say that his is the only solution to the problem.”

Yukawa’s irritation was plain from his unusually hard tone. Kusanagi had rarely seen the levelheaded physicist this agitated.

“So you think Ishigami’s lying? He’s not the murderer?”

Yukawa frowned and lowered his eyes.

“What’s your basis for saying that?” the detective went on. “If you’ve got a theory of your own, I’d like to hear it. Or is it just that you can’t bear to think of your old friend as a killer?”

Yukawa stood and turned his back to Kusanagi.

“Yukawa?”

“It’s true. I don’t want to believe it,” Yukawa said. “Like I said before, that man is made of logic. Emotion comes a distant second. He’s capable of doing anything if he thinks it’s an effective solution to the problem at hand. Still, it’s very hard for me to imagine him going so far as to murder someone—especially someone with whom he had no personal connection.”

“And that’s your basis for refuting his story?”

Yukawa spun back around and glared at the detective. But his eyes were filled with sadness, not anger.

“There are some things in life that we have to accept as truth, even though we don’t want to believe them. I know that.”

“And still you think Ishigami’s innocent?”

Yukawa’s face twisted, and he shook his head. “I wouldn’t say that.”

“I know what you think happened. You think it was Yasuko Hanaoka who killed Togashi, and Ishigami’s been trying to protect her. But the more we’ve looked into it, the less likely that scenario seems to be. We have several pieces of evidence pointing to Ishigami’s being a stalker—so much that it would have been very hard to fake, no matter how enthusiastic he was about protecting her. Besides, how many people are there who would willingly take the blame for something like murder? Yasuko isn’t Ishigami’s wife or part of his family. She’s not even his lover. Say he had wanted to protect her, and in fact helped conceal the murder—when all that fell apart, most people would resign themselves to their failure at that point. It’s only human.”

Yukawa’s eyes widened, as though from a sudden realization. “Yes,” he muttered. “People give up when things go bad. It would be nearly impossible to protect someone to the bitter end like he would have had to do.” He gazed off into the distance. “Hard even for Ishigami. And he knows it. That’s why—”

“What?”

“No.” Yukawa shook his head. “Nothing.”

“As I see it, we have to accept that Ishigami did it. And unless some new facts come to light, I don’t see this investigation going in a different direction.”

Yukawa rubbed his face with his hands. He breathed a long quiet sigh. “He’s chosen this,” he said at last. “He’s chosen to spend the rest of his days in prison.”

“It’s not really a choice now that he’s killed someone.”

“Indeed,” Yukawa whispered. He stood still for some time, his head hanging. Then, without moving, he said, “I’m sorry, but maybe you could leave me alone for a while. I’m tired.”

Something was definitely wrong with Yukawa. Kusanagi wanted to ask more questions, but instead he rose from his chair in silence. His friend did look terribly exhausted.

Kusanagi left Laboratory 13 and made his way down the dimly lit hallway. At the top of the stairs he ran into a student. Kusanagi recognized the young man’s thin, nervous face. He was a graduate student, one of Yukawa’s; his name was Tokiwa. He was the one who had told Kusanagi that Yukawa had gone to Shinozaki the last time the detective had dropped by the laboratory.

Tokiwa nodded slightly as he walked by.

“Hey there,” Kusanagi called out. Tokiwa turned around, a look of confusion on his face, and the detective smiled at him. “Do you have a moment? There was something I wanted to ask you.”

Tokiwa checked his wristwatch and said yes, he had a little time.

They left the physics building and went to the nearest cafeteria, one frequented mostly by students in the sciences. Kusanagi bought them both coffee from a vending machine and sat down across from Tokiwa.

“This is way better than the instant stuff you guys drink in that lab,” the detective observed, taking a sip from his paper cup.

Tokiwa smiled, but his face was still tense.

So much for breaking the ice. Kusanagi inwardly debated chatting with the student for a little longer, but he decided it would only be a waste of time, so he got down to business. “I wanted to ask you about Assistant Professor Yukawa, actually. Have you noticed anything odd about him lately?”

Tokiwa was clearly bewildered by the question. Kusanagi immediately regretted his own directness, but what was done was done. “I mean, has he been looking into anything unrelated to his university work, or gone anywhere unusual?”

Tokiwa scratched his jaw. He seemed to be seriously considering the question, at least.

Kusanagi tried smiling at him. “Don’t worry, he’s not involved in an investigation or anything. It is a little hard to explain, but I can’t help getting the feeling that Yukawa is hiding something from me—because he thinks I’m better off not knowing it. I’ve tried asking, but you know how stubborn he can be.”

Kusanagi wasn’t sure how well he was getting his point across, but the student did seem to be warming to him slightly. Perhaps mentioning his professor’s stubbornness had struck a chord.

“Well,” Tokiwa began, “I’m not sure what he was researching, but Professor Yukawa was on the phone to the library a few days ago.”

“The library? You mean the university’s?”

Tokiwa nodded. “I think he was asking them whether they had newspapers.”

“Newspapers? Don’t all libraries have newspapers?”

“They do, but he wanted to know how long they kept their old newspapers.”

“You don’t say.”

“Yeah. Not that he was looking for anything particularly old. I heard him asking whether he could read all the newspapers from this month. Something like that.”

“This month? Do you have any idea whether they had what he was looking for?”

“I’m pretty sure they did, because he went to the library straight after that.”

Kusanagi nodded, thanked Tokiwa, and stood up, his cup of coffee in his hand. The paper cup was still half full.

*   *   *